# rmevspec: Random samples from spectral distributions of multivariate... In mev: Modelling of Extreme Values

 rmevspec R Documentation

## Random samples from spectral distributions of multivariate extreme value models.

### Description

Generate from Qi, the spectral measure of a given multivariate extreme value model based on the L1 norm.

### Usage

```rmevspec(
n,
d,
param,
sigma,
model = c("log", "neglog", "bilog", "negbilog", "hr", "br", "xstud", "smith",
"schlather", "ct", "sdir", "dirmix", "pairbeta", "pairexp", "wdirbs", "wexpbs"),
weights = NULL,
vario = NULL,
coord = NULL,
grid = FALSE,
dist = NULL,
...
)
```

### Arguments

 `n` number of observations `d` dimension of sample `param` parameter vector for the logistic, bilogistic, negative bilogistic and extremal Dirichlet (Coles and Tawn) model. Parameter matrix for the Dirichlet mixture. Degree of freedoms for extremal student model. See Details. `sigma` covariance matrix for Brown-Resnick and extremal Student-t distributions. Symmetric matrix of squared coefficients λ^2 for the Husler-Reiss model, with zero diagonal elements. `model` for multivariate extreme value distributions, users can choose between 1-parameter logistic and negative logistic, asymmetric logistic and negative logistic, bilogistic, Husler-Reiss, extremal Dirichlet model (Coles and Tawn) or the Dirichlet mixture. Spatial models include the Brown-Resnick, Smith, Schlather and extremal Student max-stable processes. `weights` vector of length `m` for the `m` mixture components. Must sum to one `vario` semivariogram function whose first argument must be distance. Used only if provided in conjunction with `coord` and if `sigma` is missing `coord` `d` by `k` matrix of coordinates, used as input in the variogram `vario` or as parameter for the Smith model. If `grid` is `TRUE`, unique entries should be supplied. `grid` Logical. `TRUE` if the coordinates are two-dimensional grid points (spatial models). `dist` symmetric matrix of pairwise distances. Default to `NULL`. `...` additional arguments for the `vario` function

### Details

The vector param differs depending on the model

• `log`: one dimensional parameter greater than 1

• `neglog`: one dimensional positive parameter

• `bilog`: `d`-dimensional vector of parameters in [0,1]

• `negbilog`: `d`-dimensional vector of negative parameters

• `ct`, `dir`, `negdir`: `d`-dimensional vector of positive (a)symmetry parameters. Alternatively, a d+1 vector consisting of the `d` Dirichlet parameters and the last entry is an index of regular variation in (0, 1] treated as scale

• `xstud`: one dimensional parameter corresponding to degrees of freedom `alpha`

• `dirmix`: `d` by `m`-dimensional matrix of positive (a)symmetry parameters

• `pairbeta, pairexp`: `d(d-1)/2+1` vector of parameters, containing the concentration parameter and the coefficients of the pairwise beta, in lexicographical order e.g., β_{1,2}, β_{1,3}, …

• `wdirbs, wexpbs`: `2d` vector of `d` concentration parameters followed by the `d` Dirichlet parameters

### Value

an `n` by `d` exact sample from the corresponding multivariate extreme value model

### Note

This functionality can be useful to generate for example Pareto processes with marginal exceedances.

Leo Belzile

### References

Dombry, Engelke and Oesting (2016). Exact simulation of max-stable processes, Biometrika, 103(2), 303–317.

Boldi (2009). A note on the representation of parametric models for multivariate extremes. Extremes 12, 211–218.

### Examples

```set.seed(1)
rmevspec(n=100, d=3, param=2.5, model='log')
rmevspec(n=100, d=3, param=2.5, model='neglog')
rmevspec(n=100, d=4, param=c(0.2,0.1,0.9,0.5), model='bilog')
rmevspec(n=100, d=2, param=c(0.8,1.2), model='ct') #Dirichlet model
rmevspec(n=100, d=2, param=c(0.8,1.2,0.5), model='sdir') #with additional scale parameter
#Variogram gamma(h) = scale*||h||^alpha
#NEW: Variogram must take distance as argument
vario <- function(x, scale=0.5, alpha=0.8){ scale*x^alpha }
#grid specification
grid.coord <- as.matrix(expand.grid(runif(4), runif(4)))
rmevspec(n=100, vario=vario,coord=grid.coord, model='br')
## Example with Dirichlet mixture
alpha.mat <- cbind(c(2,1,1),c(1,2,1),c(1,1,2))
rmevspec(n=100, param=alpha.mat, weights=rep(1/3,3), model='dirmix')
```

mev documentation built on April 26, 2022, 1:07 a.m.